Question

In a non-ideal reactor modeled by the dispersion model, Peclet number represents:

• A. Ratio of convection to dispersion
• B. Ratio of diffusion to reaction rate
• C. Ratio of reaction to heat transfer
• D. Ratio of mass transfer to reaction

Hint:

Be careful to distinguish the reactor Peclet number (\( Pe = uL/D \)) from the grid or particle Peclet number (\( Pe_p = udp/D \)).
The reactor Peclet number is the reciprocal of the vessel dispersion number: \( Pe = 1 / D^* \).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the physical significance of the Peclet number (\( Pe \)) when used in the axial dispersion model to describe non-ideal reactor behavior.

Step 2: Key Formula or Approach:
The axial dispersion model uses a one-dimensional transport equation to describe back-mixing in fluid flow.
The dimensionless Peclet number for mass transfer in a reactor of length \( L \) is defined as:
\[ Pe = \frac{u \cdot L}{D} \]
where \( u \) is the average fluid velocity, \( L \) is the reactor length, and \( D \) is the axial dispersion coefficient.

Step 3: Detailed Explanation:

• Convective Transport Rate: The numerator \( u \cdot L \) is proportional to the rate of mass transport by bulk fluid flow (convection or advection).

• Dispersive Transport Rate: The denominator \( D \) represents the rate of mass transport by axial dispersion (back-mixing).

• The Ratio: Therefore, the Peclet number represents the ratio of convective transport to dispersive transport:
\[ Pe = \frac{\text{Rate of transport by convection}}{\text{Rate of transport by dispersion}} \]

• Limiting Cases:
If \( Pe \to \infty \), convection dominates entirely and dispersion is negligible, which corresponds to ideal plug flow.
If \( Pe \to 0 \), dispersion dominates, representing complete back-mixing (ideal CSTR).


Step 4: Final Answer:
The Peclet number in the dispersion model represents the ratio of convection to dispersion.